Is the following situation possible? If so, determine their present ag

1.	Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Answer» Let the age of one of the friends be ‘x’. Age of another friend is (20 – x). 4 years back age of 1st friend is (x – 4) 4 years back age of 2nd friend = (20 – x – 4) = (16 – x) Product of their ages is 48. ∴ (x – 4) (16 – x) = 48 16x – x² – 64 + 4x = 48 -x² + 20x – 64 = 48 -x² + 20x – 64 – 48 = 0 -x² + 20x – 112 = 0 x² – 20x + 112 = 0 Here, a = 1, b = -20, c = 112 b² – 4ac = (-20)² – 4( 1)( 112) = 400 – 448 = – 48 Here, b² – 4ac = -48 < 0. ∴ It has no real roots. ∴ This situation is not possible.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Answer»

Let the age of one of the friends be ‘x’.

Age of another friend is (20 – x).

4 years back age of 1st friend is (x – 4)

4 years back age of 2nd friend = (20 – x – 4)

= (16 – x)

Product of their ages is 48.

∴ (x – 4) (16 – x) = 48

16x – x² – 64 + 4x = 48

-x² + 20x – 64 = 48

-x² + 20x – 64 – 48 = 0

-x² + 20x – 112 = 0

x² – 20x + 112 = 0

Here, a = 1, b = -20, c = 112

b² – 4ac = (-20)² – 4( 1)( 112) = 400 – 448 = – 48

Here, b² – 4ac = -48 < 0.

∴ It has no real roots.

∴ This situation is not possible.